Speaking during Parliament's special tribute to the former Second Deputy Prime Minister on Tuesday, Balaam said Ali had resisted calls to retire from active politics despite concerns about his age and health, insisting that voters should determine his political future.
"I told him not to stand again, but he said, 'The people will decide,'" Balaam told Parliament.
The minister said Ali faced stiff competition during the NRM primaries in Adjumani District, where divisions within the ruling party had intensified the contest.
According to Balaam, Ali was at risk of losing the party nomination before Museveni intervened.
"The President said, 'I can't let my brother, who cannot speak louder, be defeated by young people.' He asked me to go and support him," Balaam said.
He said the intervention helped Ali secure the NRM flag.
Barugahara further disclosed that Museveni again directed him to return to Adjumani on the eve of the general election to support Ali's campaign.
"The day before the election, the President told me, 'Go back to Adjumani and conclude the game,'" he said.
Ali went on to retain the Adjumani West parliamentary seat, extending a political career that spanned more than five decades.
Barugahara also paid a personal tribute to the veteran politician, describing him as a generous mentor who treated him like family.
He recalled that Ali once gave him two cows as a personal gift.
"I'm giving you two cows, not as a minister but as my son," Barugahara quoted Ali as saying.
He added that Ali had encouraged him to support the construction of a bridge linking Moyo and Adjumani districts, a project he pledged the government would pursue.
"If this government doesn't do it, we shall work on the bridge between Moyo and Adjumani," he said.
Barugahara urged Uganda to celebrate national leaders while they are still alive rather than waiting until after their death.
"We should not talk good about them when they go. We should honour them when they are alive and give them whatever they need while they are alive," he said.
Gen Moses Ali, popularly known as the "Cock of Madi", died on Saturday at Nakasero Hospital, bringing to a close a public career that spanned more than 50 years.
Born in Adjumani District in 1939, Ali served as Finance Minister during the Idi Amin administration before leading the Uganda National Rescue Front (UNRF), a rebel group that fought the government of Milton Obote after Amin's overthrow.
Following negotiations with President Museveni's National Resistance Movement after it came to power in 1986, Ali signed a peace agreement that integrated UNRF fighters into the national army, becoming part of one of Uganda's earliest post-conflict reconciliation efforts.
He later served in several senior Cabinet positions, including Minister for Disaster Preparedness and Refugees and First Deputy Prime Minister, while representing Adjumani West in Parliament for decades.
Widely respected across the political divide, Ali was regarded as the political patriarch of the West Nile sub-region and remained an influential figure in national affairs well into his eighties.
Following the parliamentary tribute, his body was scheduled to be taken to Kololo Ceremonial Grounds for a public vigil before burial in Adjumani District.